Quantile Regression and Homogeneity Identification of a Semiparametric Panel Data Model

In this article, we delve into the quantile regression and homogeneity detection of a varying index coefficient panel data model, which incorporates fixed individual effects and exhibits nonlinear time trends. Using spline approximation, we obtain estimators for the trend functions, link functions, and index parameters, and subsequently establish the corresponding convergence rates and asymptotic normality. Observing that subjects within a group may share identical trend functions, we are motivated to further explore potential homogeneity in these trends. To this end, we propose a homogeneity identification algorithm based on binary segmentation. For the determination of the thresholding parameter in homogeneity identification, we propose a generalized Bayesian information criterion. Furthermore, we introduce a penalized method to discern the constant and linear structures within the nonparametric functions of our model. By leveraging grouped observations, we achieve more efficient estimation and improve the asymptotic properties of the estimators. To demonstrate the finite sample performance of our proposed approach, we conduct simulation studies and apply our methodology to a real-world dataset comprising Air Pollution Data and Integrated Surface Data (APD&ISD). Supplementary materials for this article are available online.